A wire of length L and radius a rigidlyl fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is L, if another wire of same material but of length 2 L and radius 2 a is stretched with a force 2 F, the increase in its length will be

Options

A. l
B. 2 l
C. l/2
D. 4 l

Answer

A

Explanation

Applying Hooke's law, we get
`y_(1)=(F)/(pir^(2))xx(L)/(DeltaL)`
and `Y_(2)=(2F)/(pi(2r)^(2))xx(2L)/(DeltaL')`
`=(FL)/(pir^(2)DeltaL')`
But `Y_(1)=Y_(2)`
So, `DeltaL'=DeltaL=l`